From Entangled Clocks to Local Realism and Hidden Variables
Why perfect entanglement correlations naturally suggest predetermined answers, what locality and realism mean, and why Einstein was led to the idea of hidden variables.
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Tag: entanglement
Long-form notes, Qiskit experiments, and applied optimization thinking.
Using the CNOT Gate to Entangle Qubits
A step-by-step study of Bernhardt's example showing how an initially unentangled pair of qubits becomes the Bell state through a CNOT gate, beginning with the tensor product and following the calculation explicitly.
Read note →From Coherence to Decoherence, Collapse and the Measurement Problem
A step-by-step distinction between coherence, decoherence and wavefunction collapse. Starting from a single electron with no definite pre-measurement path, the note shows how interaction with an environment creates entanglement, why orthogonal environmental states suppress interference, why decoherence does not select one outcome, and why this leads to the quantum measurement problem.
Read note →Why Which-Path Detection Destroys Interference: The Physical Mechanism
Why does measuring which slit an electron passes through destroy interference? The answer is not human observation or the electron somehow noticing a detector. A physical interaction correlates the electron's paths with different detector states. The overlap between those detector states directly controls the surviving interference.
Read note →Measuring Entangled Qubits in Same and Different Bases
Entanglement becomes much clearer when we stop treating it only as a factorization test and start asking what Alice and Bob actually observe when they measure. This note develops the Bell-state measurement behavior step by step, showing why same-basis measurements are perfectly correlated while different-basis measurements become 50/50.
Read note →Tensor Products and Entanglement: Why Two Qubits Need a Joint State
Tensor products answer a basic question in quantum mechanics: how do we describe two quantum systems together? This note develops tensor products from scratch, shows why two qubits require a four-dimensional joint state space, and explains why a pure two-qubit state is entangled when it cannot be factored into separate pure states for Alice and Bob.
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